Information Theory, Ecosystems, and Schrodinger’s Paradox

Many biological systems seem driven to have high complexity, often accompanied by low entropy. Prominent examples over evolutionary timescales include the major transitions in organismal complexity, e.g., the jump from primordial soup to DNA (prokaryotes), the introduction of multipleorganelles in the same cell, and the introduction of the epigenome. If complexity is bounded below, then if a system starts with low complexity, simple stochastic drift in the value of complexity would result in its expected complexity rising in time (Gray et al. 2010, Krakauer 2011 and references therein). However most systems initialized with low complexity stay at low complexity (e.g., ideal gases). Moreover, most systems initialized with high complexity quickly simplify, as their entropy increases. The question is what distinguishes such systems, such as the many examples of biological systems that appear driven to achieve and maintain high complexity. Many processes can drive complexity increases / entropy decreases in biological systems. These include natural selection and adaptation, auto-catalysis, constructive neutral evolution, and embryogenesis. The second law of thermodynamics does not prohibit any of these processes even though they decrease entropy, since the biological systems in which they arise are open systems. However the second law may in fact underlie these processes, at a fundamental level. This possibility is known as “Schrodinger’s paradox” (Schrodinger 1944). Maynard Smith argued non-quantitatively that each major increase in organism complexity increased how much information is stored in the organism, and how much flows from higher to lower scales (Maynard Smith 1970, Maynard Smith 2000). This suggests that information theory is key to understanding these complexity increases. In addition, one can define complexity in information-theoretic terms, as the project leader has recently elaborated (Wolpert 2012). Finally, thermodynamics itself (including the second law) can be cast in terms of information theory. In light of this, we propose that information theory is the key to relating biological complexity increases and thermodynamics. ​